MinT - Best Known (110−35, 110, s)-Nets in Base 5

Best Known (110−35, 110, s)-Nets in Base 5

(110−35, 110, 296)-Net over F₅ — Constructive and digital

Digital (75, 110, 296)-net over F₅, using

2 times m-reduction [i] based on digital (75, 112, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 56, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(110−35, 110, 635)-Net over F₅ — Digital

Digital (75, 110, 635)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−35, 110, 54377)-Net in Base 5 — Upper bound on s

There is no (75, 110, 54378)-net in base 5, because

1 times m-reduction [i] would yield (75, 109, 54378)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15410 230568 242857 678329 807005 563493 477329 266487 484586 901144 463672 961618 547625 > 5¹⁰⁹ [i]